What is the approximate combined mole fraction of N_2 and O_2 in Earth's atmosphere?

• A. 0.25
• B. 0.99
• C. 0.50
• D. 0.75

Answer: (B)

Verified step by step guidance

1. Recall that the mole fraction of a component in a mixture is defined as the ratio of the number of moles of that component to the total number of moles of all components in the mixture. Mathematically, for component i, it is \(X_i = \frac{n_i}{n_{total}}\).
2. Identify the major components of Earth's atmosphere relevant to this problem, which are primarily nitrogen (\(N_2\)) and oxygen (\(O_2\)). Other gases like argon, carbon dioxide, and trace gases are present in much smaller amounts.
3. Use known approximate volume or mole percentages of these gases in dry air: nitrogen is about 78% and oxygen is about 21%. Since volume percentages for gases at the same conditions correspond closely to mole fractions, these percentages can be used as mole fractions.
4. Calculate the combined mole fraction of \(N_2\) and \(O_2\) by adding their individual mole fractions: \(X_{N_2 + O_2} = X_{N_2} + X_{O_2}\).
5. Sum the values: \$0.78 + 0.21$ to find the approximate combined mole fraction of nitrogen and oxygen in Earth's atmosphere.